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1 Numbers and the number system

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11 topics · 65 learning objectives

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  1. 1.1 Integers

    1. understand and use integers (positive, negative and zero)

    2. understand place value

    3. use directed numbers in practical situations e.g. temperatures

    4. order integers

    5. use the four rules of addition, subtraction, multiplication and division

    6. use brackets and the hierarchy of operations

    7. use the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’

    8. identify prime factors, common factors and common multiples

  2. 1.2 Fractions

    1. understand and use equivalent fractions, simplifying a fraction by cancelling common factors and expressing it in its simplest form (lowest terms)

    2. understand and use mixed numbers and vulgar fractions

    3. identify common denominators

    4. order fractions and calculate a given fraction of a given quantity

    5. express a given number as a fraction of another number

    6. use common denominators to add and subtract fractions and mixed numbers

    7. convert a fraction to a decimal or a percentage

    8. understand and use unit fractions as multiplicative inverses

    9. multiply and divide fractions and mixed numbers

  3. 1.3 Decimals

    1. use decimal notation

    2. understand place value

    3. order decimals

    4. convert a decimal to a fraction or a percentage Terminating decimals only

    5. recognise that a terminating decimal is a fraction

    6. convert recurring decimals into fractions

  4. 1.4 Powers and roots

    1. identify square numbers and cube numbers

    2. calculate squares, square roots, cubes and cube roots

    3. use index notation and index laws for multiplication and division of positive and negative integer powers including zero

    4. express integers as a product of powers of prime factors

    5. find highest common factors (HCF) and lowest common multiples (LCM)

    6. understand the meaning of surds

    7. manipulate surds, including rationalising a denominator

    8. use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

  5. 1.5 Set language and notation

    1. understand the definition of a set

    2. use the set notation ∪, ∩, ∈ and ∉, with E for the universal set and ∅ for the empty set

    3. understand the concept of the universal set and the empty set and the symbols for these sets

    4. understand and use the complement of a set, using the notation A'

    5. use Venn diagrams to represent sets

    6. understand sets defined in algebraic terms, and understand and use subsets; if A is a subset of B, use A ⊂ B

    7. use Venn diagrams to represent sets and the number of elements in sets

    8. use the notation n(A) for the number of elements in the set A

    9. use sets in practical situations

  6. 1.6 Percentages

    1. Understand that a percentage is a number of parts per 100.

    2. express a given number as a percentage of another number

    3. express a percentage as a fraction and as a decimal

    4. understand the multiplicative nature of percentages as operators

    5. solve simple percentage problems, including percentage increase and decrease

    6. use reverse percentages In a sale, prices were reduced by 30%. The sale price of an item was £17.50 Calculate the original price of the item

    7. use compound interest and depreciation

    8. use repeated percentage change Calculate the total percentage increase when an increase of 30% is followed by a decrease of 20%

    9. solve compound interest problems

  7. 1.7 Ratio and proportion

    1. use ratio notation, including reduction to its simplest form and its various links to fraction notation Express in the form 1 : n

    2. divide a quantity in a given ratio or ratios Share £416 in the ratio 5 : 3 or 4 : 3 : 1

    3. use the process of proportionality to evaluate unknown quantities

    4. Calculate an unknown quantity when quantities vary in direct proportion, including completing a value table.

    5. solve word problems about ratio and proportion Including maps and scale diagrams

  8. 1.8 Degree of accuracy

    1. 1.8.ARound integers to a given power of 10

      round integers to a given power of 10

    2. 1.8.BRounding to significant figures or decimal places

      round to a given number of significant figures or decimal places

    3. 1.8.CUpper and lower bounds

      identify upper and lower bounds where values are given to a degree of accuracy

    4. 1.8.DEstimating numerical calculations

      Use estimation, including rounding values to one significant figure, to evaluate numerical approximations.

    5. 1.8.HAUpper- and lower-bound problems

      Solve upper- and lower-bound problems when values are given to a stated degree of accuracy.

  9. 1.9 Standard form

    1. calculate with and interpret numbers in the form a × 10ⁿ, where n is an integer and 1 ≤ a < 10

    2. solve problems involving standard form

  10. 1.10 Applying number

    1. use and apply number in everyday personal, domestic or community life

    2. Carry out calculations using metric units of mass, length, area, volume and capacity.

    3. Carry out calculations with time and money, including currency conversion.

  11. 1.11 Electronic calculators

    1. Use a scientific electronic calculator to determine numerical results.